An Introduction to Mathematical Statistics and Its Applications (6th Edition)

Published by Pearson
ISBN 10: 0-13411-421-3
ISBN 13: 978-0-13411-421-7

Chapter 2 Probability - 2.2 Sample Spaces and the Algebra of Sets - Questions - Page 19: 3

Answer

$$A = \{ 134, 135, 136, 234, 235, 236 \}$$

Work Step by Step

1. Write the sample space: $S = \{123,124,125,126, 134, 135,136,145,146,234,235,236,245,246,256,345,346, 356, 456 \}$ If 3 is the second smallest, there must be a 2 or a 1 in the outcome, so 3 is not the smallest one, so we eliminate 345,346,356 and 456. Since it can't be the larger number, there must be a 4, 5 or 6, so we eliminate 123. And most important, there has to be a "3" in the outcome, so we eliminate: 124,125,126,145,146,245,246 and 256. $$A = \{ 134, 135, 136, 234, 235, 236 \}$$
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